Scattering of radiation by a quasiperiodic two-dimensional medium (Q1101612)

We study the scattering of radiation by a medium presenting inhomogeneities distributed in a quasiperiodic way. We show the existence of quasiperiodic solutions of the two-dimensional stationary wave equation, under certain conditions on the index of refraction, using a technique based on Dinaburg-Sinai method for one-dimensional Schrödinger equation with a quasiperiodic potential. Moreover we show that the energy spectrum contains a nonempty absolutely continuous component, with a subset having high degeneracy, provided the inhomogeneities are small enough.